/*
** $Id: lmathlib.c $
** Standard mathematical library
** See Copyright Notice in lua.h
*/

#define lmathlib_c
#define LUA_LIB

#include "lprefix.h"

#include <float.h>
#include <limits.h>
#include <math.h>
#include <stdlib.h>
#include <time.h>

#include "lua.h"

#include "lauxlib.h"
#include "lualib.h"

#undef PI
#define PI (l_mathop(3.141592653589793238462643383279502884))

static int math_abs(lua_State *L)
{
    if (lua_isinteger(L, 1)) {
        lua_Integer n = lua_tointeger(L, 1);
        if (n < 0)
            n = (lua_Integer)(0u - (lua_Unsigned)n);
        lua_pushinteger(L, n);
    } else
        lua_pushnumber(L, l_mathop(fabs)(luaL_checknumber(L, 1)));
    return 1;
}

static int math_sin(lua_State *L)
{
    lua_pushnumber(L, l_mathop(sin)(luaL_checknumber(L, 1)));
    return 1;
}

static int math_cos(lua_State *L)
{
    lua_pushnumber(L, l_mathop(cos)(luaL_checknumber(L, 1)));
    return 1;
}

static int math_tan(lua_State *L)
{
    lua_pushnumber(L, l_mathop(tan)(luaL_checknumber(L, 1)));
    return 1;
}

static int math_asin(lua_State *L)
{
    lua_pushnumber(L, l_mathop(asin)(luaL_checknumber(L, 1)));
    return 1;
}

static int math_acos(lua_State *L)
{
    lua_pushnumber(L, l_mathop(acos)(luaL_checknumber(L, 1)));
    return 1;
}

static int math_atan(lua_State *L)
{
    lua_Number y = luaL_checknumber(L, 1);
    lua_Number x = luaL_optnumber(L, 2, 1);
    lua_pushnumber(L, l_mathop(atan2)(y, x));
    return 1;
}

static int math_toint(lua_State *L)
{
    int valid;
    lua_Integer n = lua_tointegerx(L, 1, &valid);
    if (l_likely(valid))
        lua_pushinteger(L, n);
    else {
        luaL_checkany(L, 1);
        luaL_pushfail(L); /* value is not convertible to integer */
    }
    return 1;
}

static void pushnumint(lua_State *L, lua_Number d)
{
    lua_Integer n;
    if (lua_numbertointeger(d, &n)) /* does 'd' fit in an integer? */
        lua_pushinteger(L, n);      /* result is integer */
    else
        lua_pushnumber(L, d); /* result is float */
}

static int math_floor(lua_State *L)
{
    if (lua_isinteger(L, 1))
        lua_settop(L, 1); /* integer is its own floor */
    else {
        lua_Number d = l_mathop(floor)(luaL_checknumber(L, 1));
        pushnumint(L, d);
    }
    return 1;
}

static int math_ceil(lua_State *L)
{
    if (lua_isinteger(L, 1))
        lua_settop(L, 1); /* integer is its own ceil */
    else {
        lua_Number d = l_mathop(ceil)(luaL_checknumber(L, 1));
        pushnumint(L, d);
    }
    return 1;
}

static int math_fmod(lua_State *L)
{
    if (lua_isinteger(L, 1) && lua_isinteger(L, 2)) {
        lua_Integer d = lua_tointeger(L, 2);
        if ((lua_Unsigned)d + 1u <= 1u) { /* special cases: -1 or 0 */
            luaL_argcheck(L, d != 0, 2, "zero");
            lua_pushinteger(L, 0); /* avoid overflow with 0x80000... / -1 */
        } else
            lua_pushinteger(L, lua_tointeger(L, 1) % d);
    } else
        lua_pushnumber(L, l_mathop(fmod)(luaL_checknumber(L, 1),
                                         luaL_checknumber(L, 2)));
    return 1;
}

/*
** next function does not use 'modf', avoiding problems with 'double*'
** (which is not compatible with 'float*') when lua_Number is not
** 'double'.
*/
static int math_modf(lua_State *L)
{
    if (lua_isinteger(L, 1)) {
        lua_settop(L, 1);     /* number is its own integer part */
        lua_pushnumber(L, 0); /* no fractional part */
    } else {
        lua_Number n = luaL_checknumber(L, 1);
        /* integer part (rounds toward zero) */
        lua_Number ip = (n < 0) ? l_mathop(ceil)(n) : l_mathop(floor)(n);
        pushnumint(L, ip);
        /* fractional part (test needed for inf/-inf) */
        lua_pushnumber(L, (n == ip) ? l_mathop(0.0) : (n - ip));
    }
    return 2;
}

static int math_sqrt(lua_State *L)
{
    lua_pushnumber(L, l_mathop(sqrt)(luaL_checknumber(L, 1)));
    return 1;
}

static int math_ult(lua_State *L)
{
    lua_Integer a = luaL_checkinteger(L, 1);
    lua_Integer b = luaL_checkinteger(L, 2);
    lua_pushboolean(L, (lua_Unsigned)a < (lua_Unsigned)b);
    return 1;
}

static int math_log(lua_State *L)
{
    lua_Number x = luaL_checknumber(L, 1);
    lua_Number res;
    if (lua_isnoneornil(L, 2))
        res = l_mathop(log)(x);
    else {
        lua_Number base = luaL_checknumber(L, 2);
#if !defined(LUA_USE_C89)
        if (base == l_mathop(2.0))
            res = l_mathop(log2)(x);
        else
#endif
            if (base == l_mathop(10.0))
            res = l_mathop(log10)(x);
        else
            res = l_mathop(log)(x) / l_mathop(log)(base);
    }
    lua_pushnumber(L, res);
    return 1;
}

static int math_exp(lua_State *L)
{
    lua_pushnumber(L, l_mathop(exp)(luaL_checknumber(L, 1)));
    return 1;
}

static int math_deg(lua_State *L)
{
    lua_pushnumber(L, luaL_checknumber(L, 1) * (l_mathop(180.0) / PI));
    return 1;
}

static int math_rad(lua_State *L)
{
    lua_pushnumber(L, luaL_checknumber(L, 1) * (PI / l_mathop(180.0)));
    return 1;
}

static int math_min(lua_State *L)
{
    int n = lua_gettop(L); /* number of arguments */
    int imin = 1;          /* index of current minimum value */
    int i;
    luaL_argcheck(L, n >= 1, 1, "value expected");
    for (i = 2; i <= n; i++) {
        if (lua_compare(L, i, imin, LUA_OPLT))
            imin = i;
    }
    lua_pushvalue(L, imin);
    return 1;
}

static int math_max(lua_State *L)
{
    int n = lua_gettop(L); /* number of arguments */
    int imax = 1;          /* index of current maximum value */
    int i;
    luaL_argcheck(L, n >= 1, 1, "value expected");
    for (i = 2; i <= n; i++) {
        if (lua_compare(L, imax, i, LUA_OPLT))
            imax = i;
    }
    lua_pushvalue(L, imax);
    return 1;
}

static int math_type(lua_State *L)
{
    if (lua_type(L, 1) == LUA_TNUMBER)
        lua_pushstring(L, (lua_isinteger(L, 1)) ? "integer" : "float");
    else {
        luaL_checkany(L, 1);
        luaL_pushfail(L);
    }
    return 1;
}

/*
** {==================================================================
** Pseudo-Random Number Generator based on 'xoshiro256**'.
** ===================================================================
*/

/* number of binary digits in the mantissa of a float */
#define FIGS l_floatatt(MANT_DIG)

#if FIGS > 64
/* there are only 64 random bits; use them all */
#undef FIGS
#define FIGS 64
#endif

/*
** LUA_RAND32 forces the use of 32-bit integers in the implementation
** of the PRN generator (mainly for testing).
*/
#if !defined(LUA_RAND32) && !defined(Rand64)

/* try to find an integer type with at least 64 bits */

#if (ULONG_MAX >> 31 >> 31) >= 3

/* 'long' has at least 64 bits */
#define Rand64 unsigned long

#elif !defined(LUA_USE_C89) && defined(LLONG_MAX)

/* there is a 'long long' type (which must have at least 64 bits) */
#define Rand64 unsigned long long

#elif (LUA_MAXUNSIGNED >> 31 >> 31) >= 3

/* 'lua_Integer' has at least 64 bits */
#define Rand64 lua_Unsigned

#endif

#endif

#if defined(Rand64) /* { */

/*
** Standard implementation, using 64-bit integers.
** If 'Rand64' has more than 64 bits, the extra bits do not interfere
** with the 64 initial bits, except in a right shift. Moreover, the
** final result has to discard the extra bits.
*/

/* avoid using extra bits when needed */
#define trim64(x) ((x)&0xffffffffffffffffu)

/* rotate left 'x' by 'n' bits */
static Rand64 rotl(Rand64 x, int n)
{
    return (x << n) | (trim64(x) >> (64 - n));
}

static Rand64 nextrand(Rand64 *state)
{
    Rand64 state0 = state[0];
    Rand64 state1 = state[1];
    Rand64 state2 = state[2] ^ state0;
    Rand64 state3 = state[3] ^ state1;
    Rand64 res = rotl(state1 * 5, 7) * 9;
    state[0] = state0 ^ state3;
    state[1] = state1 ^ state2;
    state[2] = state2 ^ (state1 << 17);
    state[3] = rotl(state3, 45);
    return res;
}

/* must take care to not shift stuff by more than 63 slots */

/*
** Convert bits from a random integer into a float in the
** interval [0,1), getting the higher FIG bits from the
** random unsigned integer and converting that to a float.
*/

/* must throw out the extra (64 - FIGS) bits */
#define shift64_FIG (64 - FIGS)

/* to scale to [0, 1), multiply by scaleFIG = 2^(-FIGS) */
#define scaleFIG    (l_mathop(0.5) / ((Rand64)1 << (FIGS - 1)))

static lua_Number I2d(Rand64 x)
{
    return (lua_Number)(trim64(x) >> shift64_FIG) * scaleFIG;
}

/* convert a 'Rand64' to a 'lua_Unsigned' */
#define I2UInt(x) ((lua_Unsigned)trim64(x))

/* convert a 'lua_Unsigned' to a 'Rand64' */
#define Int2I(x)  ((Rand64)(x))

#else /* no 'Rand64'   }{ */

/* get an integer with at least 32 bits */
#if LUAI_IS32INT
typedef unsigned int lu_int32;
#else
typedef unsigned long lu_int32;
#endif

/*
** Use two 32-bit integers to represent a 64-bit quantity.
*/
typedef struct Rand64 {
    lu_int32 h; /* higher half */
    lu_int32 l; /* lower half */
} Rand64;

/*
** If 'lu_int32' has more than 32 bits, the extra bits do not interfere
** with the 32 initial bits, except in a right shift and comparisons.
** Moreover, the final result has to discard the extra bits.
*/

/* avoid using extra bits when needed */
#define trim32(x) ((x)&0xffffffffu)

/*
** basic operations on 'Rand64' values
*/

/* build a new Rand64 value */
static Rand64 packI(lu_int32 h, lu_int32 l)
{
    Rand64 result;
    result.h = h;
    result.l = l;
    return result;
}

/* return i << n */
static Rand64 Ishl(Rand64 i, int n)
{
    lua_assert(n > 0 && n < 32);
    return packI((i.h << n) | (trim32(i.l) >> (32 - n)), i.l << n);
}

/* i1 ^= i2 */
static void Ixor(Rand64 *i1, Rand64 i2)
{
    i1->h ^= i2.h;
    i1->l ^= i2.l;
}

/* return i1 + i2 */
static Rand64 Iadd(Rand64 i1, Rand64 i2)
{
    Rand64 result = packI(i1.h + i2.h, i1.l + i2.l);
    if (trim32(result.l) < trim32(i1.l)) /* carry? */
        result.h++;
    return result;
}

/* return i * 5 */
static Rand64 times5(Rand64 i)
{
    return Iadd(Ishl(i, 2), i); /* i * 5 == (i << 2) + i */
}

/* return i * 9 */
static Rand64 times9(Rand64 i)
{
    return Iadd(Ishl(i, 3), i); /* i * 9 == (i << 3) + i */
}

/* return 'i' rotated left 'n' bits */
static Rand64 rotl(Rand64 i, int n)
{
    lua_assert(n > 0 && n < 32);
    return packI((i.h << n) | (trim32(i.l) >> (32 - n)),
                 (trim32(i.h) >> (32 - n)) | (i.l << n));
}

/* for offsets larger than 32, rotate right by 64 - offset */
static Rand64 rotl1(Rand64 i, int n)
{
    lua_assert(n > 32 && n < 64);
    n = 64 - n;
    return packI((trim32(i.h) >> n) | (i.l << (32 - n)),
                 (i.h << (32 - n)) | (trim32(i.l) >> n));
}

/*
** implementation of 'xoshiro256**' algorithm on 'Rand64' values
*/
static Rand64 nextrand(Rand64 *state)
{
    Rand64 res = times9(rotl(times5(state[1]), 7));
    Rand64 t = Ishl(state[1], 17);
    Ixor(&state[2], state[0]);
    Ixor(&state[3], state[1]);
    Ixor(&state[1], state[2]);
    Ixor(&state[0], state[3]);
    Ixor(&state[2], t);
    state[3] = rotl1(state[3], 45);
    return res;
}

/*
** Converts a 'Rand64' into a float.
*/

/* an unsigned 1 with proper type */
#define UONE      ((lu_int32)1)

#if FIGS <= 32

/* 2^(-FIGS) */
#define scaleFIG (l_mathop(0.5) / (UONE << (FIGS - 1)))

/*
** get up to 32 bits from higher half, shifting right to
** throw out the extra bits.
*/
static lua_Number I2d(Rand64 x)
{
    lua_Number h = (lua_Number)(trim32(x.h) >> (32 - FIGS));
    return h * scaleFIG;
}

#else /* 32 < FIGS <= 64 */

/* must take care to not shift stuff by more than 31 slots */

/* 2^(-FIGS) = 1.0 / 2^30 / 2^3 / 2^(FIGS-33) */
#define scaleFIG \
    (l_mathop(1.0) / (UONE << 30) / l_mathop(8.0) / (UONE << (FIGS - 33)))

/*
** use FIGS - 32 bits from lower half, throwing out the other
** (32 - (FIGS - 32)) = (64 - FIGS) bits
*/
#define shiftLOW (64 - FIGS)

/*
** higher 32 bits go after those (FIGS - 32) bits: shiftHI = 2^(FIGS - 32)
*/
#define shiftHI  ((lua_Number)(UONE << (FIGS - 33)) * l_mathop(2.0))

static lua_Number I2d(Rand64 x)
{
    lua_Number h = (lua_Number)trim32(x.h) * shiftHI;
    lua_Number l = (lua_Number)(trim32(x.l) >> shiftLOW);
    return (h + l) * scaleFIG;
}

#endif

/* convert a 'Rand64' to a 'lua_Unsigned' */
static lua_Unsigned I2UInt(Rand64 x)
{
    return ((lua_Unsigned)trim32(x.h) << 31 << 1) | (lua_Unsigned)trim32(x.l);
}

/* convert a 'lua_Unsigned' to a 'Rand64' */
static Rand64 Int2I(lua_Unsigned n)
{
    return packI((lu_int32)(n >> 31 >> 1), (lu_int32)n);
}

#endif /* } */

/*
** A state uses four 'Rand64' values.
*/
typedef struct {
    Rand64 s[4];
} RanState;

/*
** Project the random integer 'ran' into the interval [0, n].
** Because 'ran' has 2^B possible values, the projection can only be
** uniform when the size of the interval is a power of 2 (exact
** division). Otherwise, to get a uniform projection into [0, n], we
** first compute 'lim', the smallest Mersenne number not smaller than
** 'n'. We then project 'ran' into the interval [0, lim].  If the result
** is inside [0, n], we are done. Otherwise, we try with another 'ran',
** until we have a result inside the interval.
*/
static lua_Unsigned project(lua_Unsigned ran, lua_Unsigned n,
                            RanState *state)
{
    if ((n & (n + 1)) == 0) /* is 'n + 1' a power of 2? */
        return ran & n;     /* no bias */
    else {
        lua_Unsigned lim = n;
        /* compute the smallest (2^b - 1) not smaller than 'n' */
        lim |= (lim >> 1);
        lim |= (lim >> 2);
        lim |= (lim >> 4);
        lim |= (lim >> 8);
        lim |= (lim >> 16);
#if (LUA_MAXUNSIGNED >> 31) >= 3
        lim |= (lim >> 32); /* integer type has more than 32 bits */
#endif
        lua_assert((lim & (lim + 1)) == 0     /* 'lim + 1' is a power of 2, */
                   && lim >= n                /* not smaller than 'n', */
                   && (lim >> 1) < n);        /* and it is the smallest one */
        while ((ran &= lim) > n)              /* project 'ran' into [0..lim] */
            ran = I2UInt(nextrand(state->s)); /* not inside [0..n]? try again */
        return ran;
    }
}

static int math_random(lua_State *L)
{
    lua_Integer low, up;
    lua_Unsigned p;
    RanState *state = (RanState *)lua_touserdata(L, lua_upvalueindex(1));
    Rand64 rv = nextrand(state->s);     /* next pseudo-random value */
    switch (lua_gettop(L)) {            /* check number of arguments */
        case 0: {                       /* no arguments */
            lua_pushnumber(L, I2d(rv)); /* float between 0 and 1 */
            return 1;
        }
        case 1: { /* only upper limit */
            low = 1;
            up = luaL_checkinteger(L, 1);
            if (up == 0) {                      /* single 0 as argument? */
                lua_pushinteger(L, I2UInt(rv)); /* full random integer */
                return 1;
            }
            break;
        }
        case 2: { /* lower and upper limits */
            low = luaL_checkinteger(L, 1);
            up = luaL_checkinteger(L, 2);
            break;
        }
        default:
            return luaL_error(L, "wrong number of arguments");
    }
    /* random integer in the interval [low, up] */
    luaL_argcheck(L, low <= up, 1, "interval is empty");
    /* project random integer into the interval [0, up - low] */
    p = project(I2UInt(rv), (lua_Unsigned)up - (lua_Unsigned)low, state);
    lua_pushinteger(L, p + (lua_Unsigned)low);
    return 1;
}

static void setseed(lua_State *L, Rand64 *state,
                    lua_Unsigned n1, lua_Unsigned n2)
{
    int i;
    state[0] = Int2I(n1);
    state[1] = Int2I(0xff); /* avoid a zero state */
    state[2] = Int2I(n2);
    state[3] = Int2I(0);
    for (i = 0; i < 16; i++)
        nextrand(state); /* discard initial values to "spread" seed */
    lua_pushinteger(L, n1);
    lua_pushinteger(L, n2);
}

/*
** Set a "random" seed. To get some randomness, use the current time
** and the address of 'L' (in case the machine does address space layout
** randomization).
*/
static void randseed(lua_State *L, RanState *state)
{
    lua_Unsigned seed1 = (lua_Unsigned)luaport_time(NULL);
    lua_Unsigned seed2 = (lua_Unsigned)(size_t)L;
    setseed(L, state->s, seed1, seed2);
}

static int math_randomseed(lua_State *L)
{
    RanState *state = (RanState *)lua_touserdata(L, lua_upvalueindex(1));
    if (lua_isnone(L, 1)) {
        randseed(L, state);
    } else {
        lua_Integer n1 = luaL_checkinteger(L, 1);
        lua_Integer n2 = luaL_optinteger(L, 2, 0);
        setseed(L, state->s, n1, n2);
    }
    return 2; /* return seeds */
}

static const luaL_Reg randfuncs[] = {
    { "random", math_random },
    { "randomseed", math_randomseed },
    { NULL, NULL }
};

/*
** Register the random functions and initialize their state.
*/
static void setrandfunc(lua_State *L)
{
    RanState *state = (RanState *)lua_newuserdatauv(L, sizeof(RanState), 0);
    randseed(L, state); /* initialize with a "random" seed */
    lua_pop(L, 2);      /* remove pushed seeds */
    luaL_setfuncs(L, randfuncs, 1);
}

/* }================================================================== */

/*
** {==================================================================
** Deprecated functions (for compatibility only)
** ===================================================================
*/
#if defined(LUA_COMPAT_MATHLIB)

static int math_cosh(lua_State *L)
{
    lua_pushnumber(L, l_mathop(cosh)(luaL_checknumber(L, 1)));
    return 1;
}

static int math_sinh(lua_State *L)
{
    lua_pushnumber(L, l_mathop(sinh)(luaL_checknumber(L, 1)));
    return 1;
}

static int math_tanh(lua_State *L)
{
    lua_pushnumber(L, l_mathop(tanh)(luaL_checknumber(L, 1)));
    return 1;
}

static int math_pow(lua_State *L)
{
    lua_Number x = luaL_checknumber(L, 1);
    lua_Number y = luaL_checknumber(L, 2);
    lua_pushnumber(L, l_mathop(pow)(x, y));
    return 1;
}

static int math_frexp(lua_State *L)
{
    int e;
    lua_pushnumber(L, l_mathop(frexp)(luaL_checknumber(L, 1), &e));
    lua_pushinteger(L, e);
    return 2;
}

static int math_ldexp(lua_State *L)
{
    lua_Number x = luaL_checknumber(L, 1);
    int ep = (int)luaL_checkinteger(L, 2);
    lua_pushnumber(L, l_mathop(ldexp)(x, ep));
    return 1;
}

static int math_log10(lua_State *L)
{
    lua_pushnumber(L, l_mathop(log10)(luaL_checknumber(L, 1)));
    return 1;
}

#endif
/* }================================================================== */

static const luaL_Reg mathlib[] = {
    { "abs", math_abs },
    { "acos", math_acos },
    { "asin", math_asin },
    { "atan", math_atan },
    { "ceil", math_ceil },
    { "cos", math_cos },
    { "deg", math_deg },
    { "exp", math_exp },
    { "tointeger", math_toint },
    { "floor", math_floor },
    { "fmod", math_fmod },
    { "ult", math_ult },
    { "log", math_log },
    { "max", math_max },
    { "min", math_min },
    { "modf", math_modf },
    { "rad", math_rad },
    { "sin", math_sin },
    { "sqrt", math_sqrt },
    { "tan", math_tan },
    { "type", math_type },
#if defined(LUA_COMPAT_MATHLIB)
    { "atan2", math_atan },
    { "cosh", math_cosh },
    { "sinh", math_sinh },
    { "tanh", math_tanh },
    { "pow", math_pow },
    { "frexp", math_frexp },
    { "ldexp", math_ldexp },
    { "log10", math_log10 },
#endif
    /* placeholders */
    { "random", NULL },
    { "randomseed", NULL },
    { "pi", NULL },
    { "huge", NULL },
    { "maxinteger", NULL },
    { "mininteger", NULL },
    { NULL, NULL }
};

/*
** Open math library
*/
LUAMOD_API int luaopen_math(lua_State *L)
{
    luaL_newlib(L, mathlib);
    lua_pushnumber(L, PI);
    lua_setfield(L, -2, "pi");
    lua_pushnumber(L, (lua_Number)HUGE_VAL);
    lua_setfield(L, -2, "huge");
    lua_pushinteger(L, LUA_MAXINTEGER);
    lua_setfield(L, -2, "maxinteger");
    lua_pushinteger(L, LUA_MININTEGER);
    lua_setfield(L, -2, "mininteger");
    setrandfunc(L);
    return 1;
}
